3 6 2010 12 Chinese Journal of Optics and Applied Optics Vol. 3 No. 6 Dec. 2010 1674-2915( 2010) 06-0572-08 Thermal-optical property of fore optical system in space hyper spectral imager ZHANG Yi-cha 1, 2, LIU Wei 1, HU Chun-hui 1, 2 ( 1. Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China; 2. Graduate University of Chinese Academy of Sciences, Beijing 100039, China) Abstract: The performance of a hyper spectral imager is affected severely by the turbulence of orbit temperature, which would result in the thermal elastic deformation for the fore reflective telescope in the imager. Moreover, the thermal elastic deformation of mirrors, mechanical structure of the telescope, and the resulting displacements of the mirrors would induce defocusing. Based on the present study for a type of space hyper spectral imager, a model for simulating the thermal elastic deformation of the frontal telescope was built via Finite Element Method. By simulating, the surface deviation amounts and displacements of all the mirrors under different temperature loads were worked out, and the correlation between defocusing magnitude and temperature was obtained through calculating the resulting displacements of the mirrors. The analyzing results could be used as a reference for designing thermal controlling strategy and focusing system and for doing thermal-optical experiments of the developing imager. Key words: hyper spectral imager; off-axial reflective telescope; thermal-optical property; defocusing amount : TP73; TH703 : A 1, 2, 1, 1, 2 ( 1., 130033; 2., 100039) :, ; Zernike, ; Code V,,,, : 2010-05-11; : 2010-07-13 : ( No. 05001SA050)
6 ZHANG Yi-cha, et al. : Thermal-optical property of fore optical system in 573, 107. 4 m, 106. 9 m, : ; ; ; 1 Introduction The spectral imager has shown its excellence performance in remote sensing fields since its first application in 1980s. It has developed rapidly and becomes a hot focus attracting many scientific research groups all over the world in recent years, especially the space hyper spectral imager. The space spectral imager confronts complicated technical difficulties as it must be sent to the earth orbit. Its collimating results in the lab would change after it was sent into the space due to the orbit special environment, vibration of sending, temperature turbulence and the microgravity. After analyzing all of the factors a- bove, the temperature turbulence in the space is regarded as the main problem [ 1 ] which arouses much attention. Temperature turbulence is regarded as the main factor of defocusing and is studied carefully here. In order to ascertain the thermal-optical property [ 2-4 ] of the fore optical system and assess its performance after designing the opto-mechanical system, there is a need to conduct simulating for the system. In this paper, the fore optical system is simulated and set as an example to demonstrate the common method for engineering application. The presented simulating model is built via present practical techniques [ 5-7] to find the correlation between mirrors surface deviation and temperature, and the correlation between defocusing amount and temperature, so as to give theoretical reference for the following researching phases. 2 Opto-mechanical system The hyper spectral imager discussed here consists of several spectrometers and a fore optical system, which is an off-axial reflective telescope system. According to the experiential prediction, a focusing system would be placed on the end part of the telescope. The optical system of the telescope is described by Fig. 1. Fig. 1 Schematic diagram of optical system Fig. 1 shows that the fore optical system s image position directly impacts the imaging quality of the spectrometers. It plays a key role to the imager. Fig. 2. The opto-mechanical system is described by The main structure is a lightened integral Fig. 2 Schematic diagram of main structure casting thin wall body. Three reflective mirrors are placed in the main body by supporting parts. According to the overall design, the focusing mirror can compensate the defocusing caused by thermal elastic
574 3 deformation. Therefore, it is not taken into consideration in this analyzing temporarily. However, the main structure, supporting parts and mirrors are laid more emphasis. The key point probed here is the thermal-optical property of the telescope. 3 Thermal-optical model 3. 1 Theory and simplification The thermal elastic deforming model is used to simulate the deformation of mirrors and the image position in response to the temperature turbulence. It derives from thermal elasticity theory [ 8 ], which points out that objects would deform if there is uneven temperature distribution on them or there is temperature turbulence existing relative to reference temperature. Stress and strain would exist in the structure of the objects for the same reason given above. Likewise, when there is temperature turbulence in the fore optical system, the stress and strain would generate due to different types of materials and linear expansion parameters of the components in the system. Based on the theory of thermal elasticity strictly, some assumptions and simplifications are outlined below. a. All the parts of the telescope system are complete, continuous and homogeneous ideal elastic solid. b. The displacement and deformation of the system are minute. c. Simplification of the temperature field: the space hyper spectral imager would work in a complex environment, where the temperature is turbulent during the whole orbit period because of the external radiation and the inner heat. The temperature field is not static but dynamic. However, the temperature changes slightly during the imaging period and the preparation period. So the orbit period could be divided into many short time segments. During each segment, the temperature changes slightly and could be regarded as being static. So the whole system is placed in a succession of static temperature fields, which is flying on the orbit. d. Uncoupling simplification [ 8] : when the imager flies on the orbit, temperature difference would result in expansion or shrinkage of the structure, thermal stress and strain. However, the structure would absorb or release heat while expanding or shrinking, which affects the temperature field and changes the distribution of temperature. But the heat is so limited since there is not any intense friction or plastic deformation in the whole system when the system is operating on the orbit. So the heat deriving from the deformation of the structure could be ignored. The coupled field is simplified into an approximate independent field. 3. 2 Constructing finite elements The telescope consists of main frame, mirrors, supporting parts and joining parts. It is a complex system. So it is unavailable to use a single type finite element to construct the FEM model. Among the overall factors, temperature is the main load of the optical system bears. Therefore, there is no problem with strength usually, but the key point is stiffness of the mechanical structure. The main frame is a thin wall box, which is very complicated with a lot of cross braces and holes. Since the large volume of the frame, the stiffness of the frame is the primary studying item here. After being simplified, the main frame is divided into very small 2D quadrilateral finite elements ( about 6 mm 6 mm) so as to simulate the real structure and ensure the accuracy of calculation. The constructed grid is not only similar to the real one, but also is able to ensure the harmonious matching of elements stiffness properties and smooth transition for joining areas in the grid. Athough the shapes of mirrors are very simple, the mirrors are also divided into very small hexahedral elements in order to keep the original mirror surface unchanging and offer enough nodes for surface fitting. And they also guarantees high accuracy of the
6 ZHANG Yi-cha, et al. : Thermal-optical property of fore optical system in 575 model. The supporting parts are very complicated, they could not be simplified excessively due to degrading model s accuracy. They are divided into a- bout 10 mm 10 mm 10 mm hexahedral 3D elements. Joining parts of the system provide rigid connections in joining areas. They are very important, especially the mirrors supporting areas. These areas directly affect mirrors translation and rotation. those areas are all given special treatment, and MPC ( multiple points constrain) is introduced to simulate the special joining areas. There are total 75, 968 elements in this model, which contains about 6, 000 3D elements and 88 MPC elements. 3. 3 Displacement boundary [ 9] The imager is fixed by 4 axes on the spacecraft. The mounting areas of the main body are free of constrains and can expand or shrink freely. There are only constrains in two pairs of bears in the main frame. One of the primary bears and one of the secondary bears are completely constrained, and the left bears are set free. All the nodes of the constrained primary bear are completely restrained in six freedoms, but only some nodes of the restrained secondary bear are constrained in six freedoms due to the elliptical cross-section. The axis only contacts in the short-axis direction with the secondary bear. So the nodes in the touching areas are placed in six freedoms constraint. 3. 4 Temperature load So On the hypothesis of studying thermal-optical property, only the temperature load is taken in consideration but microgravity and other factors are ignored. The reference temperature of the whole system is 18, and the temperature would fluctuate between 8 and 28 according to the engineering prediction. So discrete temperature loads are distributed between 8 and 28 in uniform. The temperature fields placed on the model are homogeneous. The static linear thermal elastic model is built on the MSC. patran software platform via FEM method based on the linear elastic theory. shown in Fig. 3. Fig. 3 FEM model of the telescope 4 Analysis and Calculation It is 4. 1 Analysis and calculation of thermal elastic deformation [ 8] The solution procedure of thermal elastic calculation is similar to common elastic calculation. The only difference is that a temperature load should be added into the physical equation. Being amended, the physical equation is xx yy zz = 1 E [ xx - ( yy + zz ) ] + T T = 1 E [ yy - ( xx + zz ) ] + T T. = 1 E [ zz - ( xx + yy ) ] + T T xy = 1 G xy, yz = 1 G yz, zx = 1 G zx ( 1) where T is temperature difference to reference point, T is thermal expansion parameter. The thermal elastic FEM equation could be deduced through adding temperature load expression into the common elastic FEM equation. The deduced formula is
576 3 u = Nq e = Bq e = D( - 0 ) = DBq e - D 0 = Sq e - D T T[ 111000] T, ( 2) where 0, q e, N, B, D, S represents strain resulted from temperature difference, nodal displacement matrix, shape function matrix, geometric matrix, elastic coefficient matrix and stress matrix, respectively. It could be obtained in the following formula by applying virtual work principle on the FEM equation. where K e p e p e 0 K e q e = p e + p e 0, ( 3) = e BT DBd = e NT Bd + = e BT D 0 d S N T pda, ( 4) e p Fig. 4 Mirrors deformation at 8 ( shrinkage) here, p e 0 represents equivalent temperature load. By inputting boundary conditions, the expected thermal elastic displacement results of the nodes in the model could be worked out through solving relational equations introduced above. All the nodes of the model stay at the original position when there is no temperature difference. Setting reference temperature, 18, as a center, apply 8, 10 28 temperature fields separately on the model, and solve the FEM function on the MSC. patran software platform separately to obtain the nodal displacement matrix, which is the expected results. Since the results are discrete, all the results can be fitted via polynomial expression to obtain the continuous results, which could be regarded as the dynamic thermal response of the model under different temperatures. Where, the deformations of the model under two boundary temperatures are described in the Fig. 4 - Fig. 7. The model s relsponses to other temperatures are distributed around the center of 18 symmetrically. The deformation results show that displacement of the system is minute, belonging to m band, which complies with the engineering prediction. Also the results indicate that the mirrors surface shape Fig. 6 Fig. 5 Mirrors deformation at 28 ( expansion) Main structure s deformation at 8 ( shrinkage) and their position both changed due to the expansion or shrinkage resulted from temperature difference.
6 ZHANG Yi-cha, et al. : Thermal-optical property of fore optical system in 577 Fig. 7 Main structure s deformation at 28 ( expansion) Fig. 9 Correlation between surface deviation and temperature of secondary mirror There results approves that temperature turbulence of the orbit is the main reason why the fore optical system defocuses. 4. 2 Surface fitting [ 5-7] Some nodes original coordinates and new coordinates after deforming are picked up from the mirrors surface, and fitted by Zernike polynomial expression. By doing that, the surface deviation( expressed in PV value and RMS value), rotation and offset of the mirrors could be obtained. The approximate correlation between surface deviation and temperature is presented by fitting the discrete surface deviation results. The correlations are shown in the Fig. 8 - Fig. 10. Fig. 8 Correlation between surface deviation and temperature of primary mirror The curves show that when the temperature rises or drops deviating from the center temperature Fig. 10 Correlation between surface deviation and temperature of third mirror 18, the surface deviation occurs. And the deviation augments while the temperature difference augmenting. However, the deviation does not exceed the limit( PV value /10, RMS value /40, =632. 8 nm) of design due to the mirrors small volume and material, nucleated glass with very small thermal expansion coefficient, which is only 1 10-7 /. These results coordinate with the engineering prediction and design requirements. 4. 3 Calculation of defocusing Some relative coefficients of the zernike polynomial expression and optical system are extracted and input into the optical design software Code-V. analyzing in Code-V, the discrete defocusing a- By mounts of the fore optical system under different temperatures are obtained, which are shown in
578 3 Tab. 1. Tab. 1 Defocusing amounts at different temperatures( flying direction is negative) Temperature / Defocusing amount/ m 8-106. 9 10-85. 6 12-64. 2 14-42. 8 16-21. 2 18 0 20 21. 4 22 42. 9 24 64. 4 26 85. 9 28 107. 4 The correlation, which is approximate linear, between temperature T and defocusing amount D could be obtained by fitting the discrete defocusing amounts. And the relation between D and T is D = 10. 6267T - 192. 083, ( 5) here the relation is demonstrated in Fig. 11, and the unit of D is m. Fig. 11 Correlation between defocusing amount and temperature According to the application requirements, the optical system s maximal allowable defocusing amount is half of a focal depth [ 10 ], which could be expressed as = 2F 2, ( 6) where is half focal depth, F is F number and is the central wavelength of the spectral range collected by the spectral imager. The fore optical system's half focal depth is =2 5. 54 2 0. 6328 m= 38. 8 m. Obviously, defocusing amount exceeds the allowable amount when the temperature difference is larger than 4, which would make image resolution decreased. Therefore, it is inevitable to adopt the measures to compensate the defocusing in order to guarantee the spectral imager s high performance. 5 Conclusions Based on the elasticity, a thermal elastic deforming model for simulating the working statement of the space hyper spectral imager in space environment is built via FEM method. After analysis and calculation, one can obtain some conclusions that a. The simulation results of the model coincide with the engineering predictions. So the model is authentic and correct in some extents. b. The results show that the design of the main frame is reasonable since the deformation, rotation and offsetting of the mirror are slight and do not exceed the design limits. The only improvement should be achieved is improving the supporting parts of the secondary mirror, because the secondary mirror rotation around the ray axis is a little large. c. When there is temperature difference, the image surface would deviate from the focal plane. The image surface would offset from the focal plane in the flying direction of the spacecraft as the temperature decreases, and the maximal offset is 106. 9 m. Contrarily, when the temperature rises, the image surface would offset to the opposite direction, and the maximal offset is 107. 4 m. When the temperature turbulence exceeds 4, amount runs out of the allowable amount. the defocusing d. It is necessary to design a focusing system for the fore optical system to compensate the system s defocus. When the focusing amount is as-
6 ZHANG Yi-cha, et al. : Thermal-optical property of fore optical system in 579 certained, the defocusing amount, errors of the model, the focusing mirror s rotation and offset resulted from temperature turbulence, and errors of assembly and measure should be considered synthetically. The focusing amount must be greater than the defocusing amount so as to give some allowance. Acknowledgement: We express our appreciation to all the people who offered help during the research. We specially thank Mr. Liuwei, who supervised the whole research. : [ 1],. [ J]., 2003, 29( 4) : 45-47. WANG H, HAN CH Y. Study on the effect applied in space remote camera of temperature[ J]. Opt. Technique, 2003, 29 ( 4) : 45-47. ( in Chinese) [ 2],,,. [ J]., 2008, 37( ) : 98-102. LI Z X, WU Q W, GAO M H, et al.. Thermal optical property of the pointing mirror in the hyper spectral imager[ J]. Infrared Laser Eng., 2008, 37( supplement) : 98-102. ( in Chinese) [ 3],,. [ J]., 2006, 32( 1) : 144-147. YANG Y, ZHANG W, CHEN SH J. Study on the thermal optics property of primary mirror applied on a space telescope [ J]. Opt. Technique, 2006, 32( 1) : 144-147. ( in Chinese) [ 4],,,. [ J]., 2001, 27( 3) : 260-265. WU Q W, LU Z SH, LU E. Study on the thermal optics property of a window applied on a space remote sensor[ J]. Opt. Technique, 2001, 27( 3) : 260-265. ( in Chinese) [ 5] GERHAED S, DAVID C, GERARD P. Advancements in interated Structural / Thermal/ Optical( STOP) analysis of optical systems[ J]. SPIE, 2007, 6675: 667500. [ 6],,,. [ J]., 2001, 9( 4) : 377-381. SHAN B ZH, CHEN E T, LU E. Thermal / structure/ optical integrated analysis of space cameras[ J]. Opt. Precision Eng., 2001, 9( 4) : 377-381. ( in Chinese) [ 7],,,. Zernike [ J]., 2007, 28( 1) : 38-42. LU F, RUAN P, MA X L, et al.. Methods of opto-mechanical analysis with Zernike polynomials[ J]. J. Appl. Opt., 2007, 28( 1) : 38-42. ( in Chinese) [ 8]. [ M]. :, 2004. ZENG P. Finite Element Analyzing and Application[ M]. Beijing: Tsinghua University Press, 2004. ( in Chinese) [ 9],,. [ J]., 2009, 17( 10) : 2450-2455. ZHANG J Q, DONG D Y, YAN CH X. Primary support of high resolution space imaging spectrometer[ J]. Opt. Precision Eng., 2009, 17( 10) : 2450-2455. ( in Chinese) [ 10],,,. [ J]., 2009, 17( 5) : 1051-1056. WANG ZH, ZHANG L P, LI CH H, et al.. Design of focusing mechanism of space tridimensional mapping camera[ J]. Opt. Precision Eng., 2009, 17( 5) : 1051-1056. ( in Chinese) : ( 1985 ),,,, CAD CAE CAM E-mail: zhych6998@ 163. com ( 1967 ),,,, E-mail: 2400liuWei@ 163. com